Question

основание трапеции равны 10 см и 20 см. диагональ отсекает от нее прямоугольный равнобедренный треугольник, гипотенузой которой является меньшее основание трапеции. вычисляете площадь этой трапеции.

Answer 1

Given Information:

We are given that the bases of the trapezoid are 10 cm and 20 cm. The diagonal of the trapezoid cuts off a right isosceles triangle, with the hypotenuse being the smaller base of the trapezoid. We need to calculate the area of this trapezoid.

Solution:

To find the area of the trapezoid, we can use the formula:

Area = (sum of the bases) * (height) / 2

In this case, the sum of the bases is 10 cm + 20 cm = 30 cm.

To find the height, we can use the Pythagorean theorem since the diagonal cuts off a right isosceles triangle. Let's denote the height as 'h' and the smaller base as 'b'. The hypotenuse of the right isosceles triangle is the smaller base, so we have:

b^2 = h^2 + h^2

Simplifying the equation, we get:

2h^2 = b^2

Taking the square root of both sides, we have:

h = sqrt(b^2 / 2)

Substituting the value of the smaller base (b = 10 cm), we get:

h = sqrt(10^2 / 2) = sqrt(100 / 2) = sqrt(50) = 5 * sqrt(2) cm

Now, we can substitute the values of the sum of the bases (30 cm) and the height (5 * sqrt(2) cm) into the formula for the area:

Area = (30 cm) * (5 * sqrt(2) cm) / 2 = 75 * sqrt(2) cm^2

Therefore, the area of the trapezoid is 75 * sqrt(2) cm^2.

Answer:

The area of the trapezoid is 75 * sqrt(2) cm^2.